Vibratory sensors, such as vibratory densitometers and vibratory viscometers, operate by detecting motion of a vibrating element that vibrates in the presence of a fluid to be characterized. The vibratory element has a vibration response that may have a vibration response parameter such as a resonant frequency or quality factor Q. The vibration response of the vibrating element is generally affected by the combined mass, stiffness, and damping characteristics of the vibrating element in combination with the fluid. Properties associated with the fluid, such as density, viscosity, temperature and the like, can be determined by processing a vibration signal or signals received from one or more motion transducers associated with the vibrating element. The processing of the vibration signal may include determining the vibration response parameter.
FIG. 1 shows a prior art vibratory sensor comprising a vibratory element and meter electronics coupled to the vibratory element. The prior art vibratory sensor includes a driver for vibrating the vibratory element and a pickoff that creates a vibration signal in response to the vibration. The vibration signal is typically a continuous time or analog signal. The meter electronics receives the vibration signal and processes the vibration signal to generate one or more fluid characteristics or fluid measurements. The meter electronics determines both the frequency and the amplitude of the vibration signal. The frequency and amplitude of the vibration signal can be further processed to determine a density of the fluid.
The prior art vibratory sensor provides a drive signal for the driver using a closed-loop circuit. The drive signal is typically based on the received vibration signal. The prior art closed-loop circuit modifies or incorporates the vibration signal or parameters of the vibration signal into the drive signal. For example, the drive signal may be an amplified, modulated, or an otherwise modified version of the received vibration signal. The received vibration signal can therefore comprise a feedback that enables the closed-loop circuit to achieve a target frequency. Using the feedback, the closed-loop circuit incrementally changes the drive frequency and monitors the vibration signal until the target frequency is reached.
Fluid properties, such as the viscosity and density of the fluid, can be determined from the frequencies where the phase difference between the drive signal and the vibration signal is 135° and 45°. These desired phase differences, denoted as first off-resonant phase difference ϕ1 and second off-resonant phase difference ϕ2, can correspond to the half power or 3 dB frequencies. The first off-resonant frequency ω1 is defined as a frequency where the first off-resonant phase difference ϕ1 is 135°. The second off-resonant frequency ω2 is defined as a frequency where the second off-resonant phase difference ϕ2 is 45°. Density measurements made at the second off-resonant frequency ω2 can be independent of fluid viscosity. Accordingly, density measurements made where the second off-resonant phase difference ϕ2 is 45° can be more accurate than density measurements made at other phase differences.
The first and second off-resonant phase differences ϕ1, ϕ2 are typically not known prior to measurement. Accordingly, the closed-loop circuit must incrementally approach the first and second off-resonant phase differences ϕ1, ϕ2 using the feedback as described in the foregoing. The incremental approach associated with the closed-loop circuit can cause a delay in determining the vibration response parameter and, therefore, cause a delay in determining the viscosity, density, or other properties of the fluid. The delays in determining such measurements can be prohibitively expensive in many applications of the vibratory sensor.
Accordingly, there is a need for determining a vibration response parameter of a vibratory element. There is also a need for determining the vibration response parameter in a desirably fast and accurate manner.